The width of the rectangle is 28 in. _________________________________________________________ Explanation: _________________________________________________________ The formula for the area, "A", of a rectangle:
Area (A) = length (L) * width (w) ;
that is: " A = L * w " ;
A = 980 in² (given);
ratio of the length to the width is: " 5 : 4 " (given);
→ Find the length (L) and the width (w). _________________________________________________________
→ 980 in² = (5x) * (4x) ;
in which: " 980 in² " is the area of the triangle;
" 5x" = the length (L) of the rectangle, for which we shall solve;
" 4x" = the width (w) of the rectangle, for which we shall solve. _______________________________________________________ If we find solve for "x" ; we can solve for "5x" and "4x" (the "length" and the "width", respectively); by plugging in the solved value for "x" ; _______________________________________________________
Divide each side by "10" ; by canceling out a "0" on each side of the equation:
→ 2x² = 98 ;
Now, divide each side of the equation by "2" ;
→ 2x² / 2 = 98 / 2 ;
to get:
→ x² = 49 ;
Now, take the "positive square root" of each side of the equation; (since a "length or width" cannot be a "negative value") ; to isolate "x" on one side of the equation; & to solve for "x" ;
→ ⁺√(x²) = √49 ;
to get:
→ x = 7 ; ______________________________________________________ Now, we can solve for the "length" and the "width" ;
→ The length is: "5x" ;
5x = 5(7) = " 35 in " ; ______________________________________________________ → The width is: "4x" ;
4x = 4(7) = "28 in." ______________________________________________________ Let us check our answer:
→ A = L * w ;
→ 980 in² = ? 35 in. * 28 in. ?? ;
Using a calculator: "35 * 28 = 980" . Yes! ; ____________________________________________________ { Also note: " in * in = in² " ? Yes! } . ____________________________________________________
